Question: Simplify the following expression: $ n = \dfrac{-3}{5} - \dfrac{1}{t - 1} $
Answer: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{t - 1}{t - 1}$ $ \dfrac{-3}{5} \times \dfrac{t - 1}{t - 1} = \dfrac{-3t + 3}{5t - 5} $ Multiply the second expression by $\dfrac{5}{5}$ $ \dfrac{1}{t - 1} \times \dfrac{5}{5} = \dfrac{5}{5t - 5} $ Therefore $ n = \dfrac{-3t + 3}{5t - 5} - \dfrac{5}{5t - 5} $ Now the expressions have the same denominator we can simply subtract the numerators: $n = \dfrac{-3t + 3 - 5 }{5t - 5} $ Distribute the negative sign: $n = \dfrac{-3t + 3 - 5}{5t - 5}$ $n = \dfrac{-3t - 2}{5t - 5}$